Heat oil in heavy large skillet over medium heat. Add shallots and sauté 15 minutes. Sprinkle with sugar and stir until shallots are golden brown, about 5 minutes. Add vinegar and boil until reduced to syrup consistency, about 1 minute. Add both broths and boil until liquid is reduced to sauce consistency, about 10 minutes. Add thyme and season with salt and pepper to taste.